(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 2kg block (m1) resting on a plane inclined 37 degrees is connected by a rope through a pulley to a block (m2) hanging free. The coefficient of static friction on m1 is 0.2. What is the mass of m2 if both masses are at rest? How about if both masses are moving at constant velocity?

2. Relevant equations

For m1:

F=mg

F=mgcosӨ

F=mgsinӨ

N=-mgcosӨ

For m2:

T=mg

3. The attempt at a solution

For m1:

F=mg=(2kg)(9.81m/s/s)=19.62N

F=mgcosӨ=19.62N(cos37)=15.66N

F=mgsinӨ=19.62N(sin37)=11.81N

N=-11.81N

F=T-mgsinӨ=0, therefore T=mgsinӨ=11.81N

Since mu=0.2, Fs=mu(N)=(0.2)(15.66N)=3.13N, therefore since Fs is less than T, the system will continue to accelerate upward.

For m2:

F=mg-T=0, therefore T=mg

If both masses are at rest, the sum of y-direction forces on m2 must equal zero, therefore for m2, T-mg=0, thus:

11.81N-m(9.81m/s/s)=0

11.81N/9.81m/s/s = m

m=1.2kg.......so in the end, does mu have any affect on the calculation of the mass for m2? Or does it and I've forgotten to calculate something?

Also if both masses are moving at constant velocity (ie: no acceleration), the mass would be same as computed above.

Thanks in advance for any tips.

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# Mass of Hanging Block

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